There have been many other movies and TV shows about a group of people who happen to get unique powers. Here are a few of them:
The 4400 - My wife and I enjoyed this USA Network show about the sudden appearance of over four thousand people who had disappeared since 1946. Not only do they reappear un-aged, but a small number of them also each possesses a unique ability. The program lasted four seasons and had an excellent cast.
Alphas - The Syfy channel's version of a superhero adventure actually is pretty good, considering it comes from the network of cheesy low-budget genre programming. A neurologist/psychologist leads a band of gifted indivuals (one has the power of "technopathy," another has the ability of "hyperkinesis," and so on) as they use their super-skills to battle bad guys who use their own powers for evil.
Fantastic Four - Marvel Comics sort of started it all by created a team from the get-go that was transformed by cosmic rays (unlike some previous super-teams who basically were pre-existing solo heroes who decided to team up.) The live action movies so far have been lackluster, but a reboot is on the way.
Heroes - This NBC television series about superpowered heroes versus superpowered villains started out so good but ended so bad. That first season, however, was superb.
Misfits of Science - Does anyone remember this show? It was a short-lived little sci-fi TV series that starred a young Courteney Cox as a telekinetic teen alongside Kevin Peter Hall as an incredible shrinking man, and Mark Thomas Miller as a super-fast guy who can shoot lightning bolts. There also was an Ice Man character in the first episode, but he didn't appear in the rest of the series apparently because of similarities to the copyrighted Marvel hero of the same name.
Mutant X - Although many thought it was a blatant rip-off of Marvel's X-Men, this show about a team of superpowered mutants was a fun little show.
No Ordinary Family - A weird storm causes a plane crash and the family on it to obtain incredible powers. Nothing really unique here, so it's no surprise that the show didn't last for very long.
X-Men - Arguably the biggest success story in this subgenre has been Marvel's uncanny group of mutant superheroes. They continue to delight fans with their ever-growing ranks of amazing characters, each with a special ability used for good or, in the case of the Brotherhood, evil.
Am I missing any good ones? Let me know.